If you just want to use Flash, then as hash hassaid you don't need to install the Windows version, just install the flashplugin-installer package. However, if you're trying to run Windows programs that themselves embed flash (but don't install it themselves), then you might actually need to install Flash in Wine. This is uncommon.

If that is your situation, then you'll want to do what the error message says and rename that file. The file is exactly where Winetricks says it is, but you may be confused since files and folders whose names start with . are hidden by default.

There, the second filename after mv is the new name for the file. I've added a .bak suffix to the file. The ~ is shorthand--recognized by the shell--that stands for the full name of your home folder (/home/jaken).

Or if you prefer to do the renaming through a graphical interface:

Open a folder window for your home folder. (This is Ubuntu's graphical file browser, Nautilus.)

Press Ctrl+H or click View > Show Hidden Files.

Go into the cache subfolder.

Go into the winetricks subfolder.

Go into the flash subfolder.

Find the entry for install_flash_player_10_active_x_.exe and rename it.

After you rename the file, you can run the Winetricks command again. It won't find the file at its usual name and location, so it will download it again. If the problem was really that the download was corrupted during download, this should fix it.

On the other hand, if the file is bad on the download server, or (more likely) if the file on the server has the same name but has been modified by Adobe since its hash was taken by the Winetricks maintainers, then you may get this error again.

If the error happens again, there may be other avenues of troubleshooting. Or you can pretend you're using Windows, download the Windows installer for Adobe Flash (you have to get the Internet Explorer / ActiveX version to have the same functionality as that file is giving you) and install it with Wine, bypassing Winetricks. (When possible it's preferable to have Wintricks automate such installations, of course.)

The problem is downloading failed, so you can download the file needed by yourself. After selecting the software or component in the Winetricks, there are logs in the terminal as follows:

You are using a 64-bit WINEPREFIX. If you encounter problems, please retest in a clean 32-bit WINEPREFIX before reporting a bug.
------------------------------------------------------
Gtk-Message: GtkDialog mapped without a transient parent. This is discouraged.
Gtk-Message: GtkDialog mapped without a transient parent. This is discouraged.
Gtk-Message: GtkDialog mapped without a transient parent. This is discouraged.
...
Downloading http://... to /home/../.cache/winetricks/...
...
sha1sum mismatch! Rename /home/../.cache/winetricks/... and try again.

Put your mouse on the string after "Downloading", it will become underlined, it's an url to download the file you need, press ctrl and click the url, it will be opened by your default browser. If it doesn't work, you can copy the url and paste it in your browser handly.

After downloading it, install it using wine:

$ wine app.exe

try the funciton you need after installation.
Then, if it doesn't work, replace the file in target folder with the file you downloaded, and try it again.(Some functions don't need to install with wine, just place them in the target directory.)

PS: If the downloading url failed, try to search it on Google to find alternative download mirrors.